The invention relates generally to detecting a gamma ray point source and, more particularly, to a method and apparatus of image reconstruction for a synthetic aperture gamma ray imager.
Radioactive materials can be detected by the gamma radiation that they produce as component radioisotopes decay. This radiation is produced from a source of radioactive materials that may be used in a nuclear device or a radiological dirty bomb, as examples. Detection of gamma radiation may take place in the presence of naturally-occurring background gamma radiation, which can originate from soil or building materials, for example. When the gamma radiation from a concentration of radioactive materials is sensed close to its source, this background radiation does not present an impediment to source detection due to the high gamma photon flux emanating from the source. When the sensing apparatus is far removed from the radiation source, though, detection of the source against the background presents challenges. When the aggregate background radiation produces counts at a higher rate than the source, a non-imaging radiation detector may not be able to detect the presence of the source at all. Even if a source is close enough to the apparatus to be detected, a non-imaging radiation detector may establish only the proximity to the point at which the detector observed the largest signal and is not typically capable of pinpointing the source location.
In applications that include stand-off mode (i.e., measured at a distance), such as, for example, in a reconnaissance operation seeking the source of radioisotopes, the total number of counts detected from the source is typically much less than the number of counts detected from background. In such a case, detection of the source may be facilitated by forming an image of the source distribution. Imaging data may be acquired when the platform on which the imaging apparatus is mounted is moving, and when this is the case, the path of the platform is called the imaging baseline. The image formed in this mode is a synthetic aperture image, and the effective aperture of this image is the imaging baseline. Thus, the synthetic aperture can be very large when compared with the dimension of the actual imaging device. This means that source, which may be in the far field of the imaging apparatus, is in the near-field of the synthetic aperture.
Forming an image from data acquired over the length of the baseline serves to distribute the background measurement over a large area, making it clear that the background of the measurement does not represent a point source. An actual point source, on the other hand, is imaged and will show in the image as a point, and so the point is made detectable despite a high aggregate background.
A mode of imaging used in some systems is known as back-projection or laminography. One approach forms a near-field image from multiple far-field images, which are functions of angle only, by extending the far-field image value at each angle to all near-field pixels (or voxels) that lie at that angle. This description applies both to the extension of a one dimensional far-field image to a two dimensional (planar) near-field image and to the extension of a two dimensional near-field image to a three dimensional (volumetric) near-field image. Such a generation of near-field imagery from far-field imagery is sometimes referred to as tomographic imaging.
One field in which tomographic imaging is widely practiced is that of emission tomography. The field of emission tomography makes use of several reconstruction approaches that include statistical reconstruction techniques based on an Expectation Maximization (EM) algorithm for iteratively computing maximum likelihood estimates of parameters in so-called “hidden data” problems. The first application of this approach to low-count emission tomography was proposed by Shepp and Vardi. Later, Hudson and Larkin found that the convergence of this algorithm could be improved; their algorithm is called the Ordered Subsets Expectation Maximization (OSEM) algorithm.
One method for producing a far-field image from the basic imaging apparatus may use standard, correlation-based coded-aperture imaging that includes using a device having an aperture composed of photon-absorbing elements positioned in front of a position-sensitive detector array (such as an Anger camera). This mode of operation is advantageous in that more than a single location on the position-sensitive detector is employed to measure photons from every direction, so that a larger number of source photons are recorded than with a parallel-hole collimator, for example. An associated disadvantage is that recorded energy from a source is spread out over a large range of angles in addition to the correct one, although the incorrectly attributed energy is spread to different angles for different PSD detector locations.
While imaging has an advantage over simple radiation counting in terms of detection, certain combinations of source and background emission rates, and source distance and total observation time, can cause images of point sources in background to fail to unambiguously image a point source. Further, although imaging may favorably increase the probability of detection, there may be a corresponding increase in the probability of a false alarm occurring. Thus, when background radiation level is high and when the false alarm rate requirement is low, detection may be difficult, and the threshold may have to be set high. The higher threshold means that many images with moderate but acceptable contrast may be errantly rejected as not having a source, or “missed.” Contrast enhancement using a point-wise, non-data-adaptive image transform can transform some of these misses into detections, but such algorithms also tend to create false detections when there is no source—which may cause the threshold to be set to an even higher threshold to reject them.
Additionally, known methods and apparatus for background removal involve making two separate measurements of the source distribution using two masks and subtracting them, prior to back-projection, to form a new measurement with zero-mean background. This is commonly referred to as mask/anti-mask subtraction, because of the optimal relationship between configurations of the two masks. However, such an approach may not improve the detectability of gamma sources and, when absorbing mask elements are non-opaque, source counts are lost in the subtraction and may result in a source that is less detectable.
Therefore, it would be desirable to design an apparatus and method of image reconstruction for a synthetic aperture gamma ray imager that results in a higher-contrast reconstructed image with enhanced source detectability in high levels of background radiation.